Skip to main content

A first order logic for partial functions

Extended abstract

  • Contributed Papers
  • Conference paper
  • First Online:
STACS 89 (STACS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 349))

Included in the following conference series:

  • 182 Accesses

Abstract

In this paper we define a first-order logic with partial functions and three thruth values (true, false, undefined). We give semantical and proof theoretical motivations for our choice of the logical consequence relation. We also present a sound and complete sequent calculus and sketch a completeness proof which is based on a tableaux method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barringer, H., Cheng, J. H., Jones, C. B.: A Logic Covering Undefinedness in Program Proofs. Acta Informatica 21 (1984), 251–269.

    Google Scholar 

  2. Beth, E. W.: The Foundations of Mathematics. North-Holland, 1959.

    Google Scholar 

  3. Broy, M., Wirsing, M.: Partial Abstract Types. Acta Informatica 18 (1982), 47–64.

    Google Scholar 

  4. Broy, M.: Equational Specification of Partial Higher-Order Algebras. Theoretical Computer Science 57 (1988), 3–45.

    Google Scholar 

  5. Goerdt, A.: Ein Hoare kalkül für getypte λ-terme. Korrektheit, Vollständigkeit, Anwendungen. Dissertation. RWTH Aachen, 1985.

    Google Scholar 

  6. Hoogewijs, A.: Partial-Predicate Logic in Computer Science. Acta Informatica 24 (1987), 381–393.

    Google Scholar 

  7. Loeckx, J.: Algorithmic Specifications: A Constructive Specification Method for Abstract Data Types. ACM Transactions on Programming languages and Systems. Vol. 9, No. 4 (1987), 646–685.

    Google Scholar 

  8. Owe, O.: An Approach to Program Reasoning Based on a First Order Logic for Partial Functions. Computer Science Technical Report Number CS-081 (Revised February 1985). Department of Electrical Engineering and Computer Sciences. University of California, San Diego.

    Google Scholar 

  9. Scott, D. S.: Outline of a Mathematical Theory of Computation Technical Monograph PRG-2, Oxford University Computing Laboratory, November 1970.

    Google Scholar 

  10. Shoenfield, J. R.: Mathematical Logic. Addison-Wesley, Reading Mass., 1967.

    Google Scholar 

  11. Smullyan, R. M.: First-Order Logic. Springer-Verlag, 1968.

    Google Scholar 

  12. Stoy, J.: Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. MIT Press, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

B. Monien R. Cori

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lucio-Carrasco, F., Gavilanes-Franco, A. (1989). A first order logic for partial functions. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028972

Download citation

  • DOI: https://doi.org/10.1007/BFb0028972

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50840-3

  • Online ISBN: 978-3-540-46098-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics